02/05/2002, 15:30 — 16:30 — Room P3.10, Mathematics Building
Miguel Abreu, Instituto Superior Técnico
Kähler metrics on symplectic toric manifolds.
As was already discussed in this seminar, a theorem of Delzant states that any symplectic manifold of dimension equipped with an effective Hamiltonian action of the standard -torus , i.e. any symplectic toric manifold, is completely determined (as a Hamiltonian -space) by the image of the moment map, a convex polytope in . In this talk I will explain, using symplectic (action-angle) coordinates, how all -compatible toric complex structures on can be effectively parametrized by smooth functions on . I will also sketch Donaldson’s formal general framework underlying this symplectic coordinates approach to Kähler toric geometry, and discuss some topics suited for application, namely: explicit construction of extremal Kähler metrics, spectral properties of toric manifolds and combinatorics of polytopes.
18/04/2002, 15:30 — 16:30 — Room P3.10, Mathematics Building
Sílvia Anjos, Instituto Superior Técnico
Toric Manifolds from Polytopes
We describe the classification of equivalence classes of symplectic toric manifolds by their moment polytopes and prove the existence part in the classification theorem by constructing symplectic toric manifolds with symplectic reduction. This construction also yields an invariant Kähler structure on every toric manifold. We conclude by analysing the transformation of a symplectic toric manifold which corresponds to a cutting of the corresponding polytope.
04/04/2002, 15:30 — 16:30 — Room P3.10, Mathematics Building
Pedro Ferreira dos Santos, Instituto Superior Técnico
Algebraic Toric Varieties
To define and study toric manifolds from the algebro-geometric viewpoint, we review basic notions of algebraic geometry, define toric varieties and explain the correspondence with fans. Several examples will be given.
21/03/2002, 15:30 — 16:30 — Room P3.10, Mathematics Building
Ana Cannas da Silva, Instituto Superior Técnico
Symplectic Toric Manifolds
Native to algebraic geometry, the study of toric manifolds has many different entrances and has been scoring a wide spectrum of applications. For symplectic geometers, they provide examples of extremely symmetric (completely integrable) hamiltonian spaces, encoded in a neat combinatorial fashion.
To define and study toric manifolds from the symplectic viewpoint, in this informal talk we review basic symplectic notions and tools, such as moment maps and symplectic reduction. We conclude by stating the list of these manifolds and by illustrating it with some famous examples.
This will be the first talk of a series in a reading seminar devoted to Toric Manifolds.
21/02/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
Marcelo Kobayashi, Instituto Superior Técnico
On the Birkhoff approach to mechanics II
07/02/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
Marcelo Kobayashi, Instituto Superior Técnico
On the Birkhoff approach to mechanics
13/11/2001, 17:00 — 18:00 — Room P3.10, Mathematics Building
Pedro Freitas, Instituto Superior Técnico
Algebraic connectivity and chromatic number of a surface
18/06/2001, 14:00 — 15:00 — Room P3.10, Mathematics Building
Giovanni Landi, Università degli studi di Trieste
Non-Commutative Spheres and Instantons
07/06/2001, 14:00 — 15:00 — Room P3.10, Mathematics Building
Esmeralda Sousa Dias, Instituto Superior Técnico
Rigid and Pseudo-Rigid Bodies: Symmetry and Reduction
17/05/2001, 14:00 — 15:00 — Room P3.10, Mathematics Building
Waldyr Oliva, Instituto Superior Técnico
Riemann Ellipsoids
General ellipsoids (with three distinct axes) are shown to be equilibrium configurarions of a self-gravitating fluid mass. Some comments on existence and stability of other equilibrium configurations (not necessarily convex) are made.
10/05/2001, 14:00 — 15:00 — Room P3.10, Mathematics Building
Rui Loja Fernandes, Instituto Superior Técnico
Hyperelliptic Prym Varieties and Integrable Systems - II
Second part of a two-part seminar on the paper Hyperelliptic Prym Varieties and Integrable Systems
19/04/2001, 14:00 — 15:00 — Room P3.10, Mathematics Building
Pedro Ferreira dos Santos, Instituto Superior Técnico
Algebraic Cycles and Homotopy Theory: an elementary overview
Algebraic cycles are classical objects in algebraic geometry. In this talk we will briefly review their definition and discuss how they can be studied using homotopy theoretic techniques.
05/04/2001, 14:00 — 15:00 — Room P3.10, Mathematics Building
Rui Loja Fernandes, Instituto Superior Técnico
Hyperelliptic Prym Varieties and Integrable Systems - I
First of two sessions on the paper Hyperelliptic Prym Varieties and Integrable Systems by R.Fernandes and P. Vanhaecke.
11/10/2000, 14:00 — 15:00 — Room P3.10, Mathematics Building
Holger Spielberg, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos
A gentle introduction to stacks
06/07/2000, 16:00 — 17:00 — Room P3.10, Mathematics Building
Sergei Anisov, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos
Towards lower bounds of Matveev complexity
08/06/2000, 15:00 — 16:00 — Room P3.10, Mathematics Building
Rosa Durão, Instituto Superior Técnico
Construção de Subvariedades Simplécticas
18/05/2000, 15:00 — 16:00 — Room P3.10, Mathematics Building
Miguel Abreu, Instituto Superior Técnico
Estruturas quase-complexas e simplectomorfismos
18/05/2000, 15:00 — 16:00 — Room P3.10, Mathematics Building
Rui Loja Fernandes, Instituto Superior Técnico
Blow-up e Invariantes de Seiberg-Witten II
04/05/2000, 15:00 — 16:00 —
Sandra Francisco, Instituto Superior Técnico
Curvas Pseudo-Holomorfas e Invariantes de Gromov
04/05/2000, 15:00 — 16:00 — Room P3.10, Mathematics Building
Rui Loja Fernandes, Instituto Superior Técnico
Blow-up e Invariantes de Seiberg-Witten